Countercurrent adsorption and simulated moving bed system

The problems posed by the motion of solid particles or a moving bed of particles in countercurrent adsorption processes have led to a number of different operational configurations. In a gas-fluidized multistage countercurrent adsorber, there are multiple sieve-tray plates in a vertical column. The adsorbent particles are fluidized by the gas stream to be cleaned entering through the perforations in the sieve tray. The fluidization level is not very vigorous. 

Let the feed fluid stream introduced into the column contain species A and B in, say, a carrier fluid. In a counter-current flow system containing two phases j = 1,2 moving 

We have already learnt via equation (8.1.36) that, for j = 1 (s, solid) being the solid/adsorhent phase moving down and j = 2 (say, v for vapor) being the fluid phase moving up, species A moves up the column and species B moves down the column if 

This result implies that species B, which is adsorbed more strongly by the adsorbent, moves down the column and species A moves up the column note that 

The next topics of interest are the operating line for the countercurrent adsorption device and the height of the device or the number of stages needed for the device to achieve a given separation. The device may be of continuous contact type or stagewise contact type. For continuous contact type devices, the approach will follow that in Section 8.1.2.3 employed for gas absorption from a concentrated gas stream. We focus on one particular species i (= A) which is being adsorbed, say, from a gas stream j = g, here the inert (solute-free) gas stream mass flow rate 

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